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McCarthy said Tuesday night that the GOP-led Congress had succeeded by bringing down Clinton's poll numbers because of the Benghazi probe

Privately, Republicans were outraged by the remarks

Washington (CNN)House Republicans on Wednesday sharply repudiated Rep. Kevin McCarthy's comments that suggested the Benghazi oversight committee had succeeded by tarnishing Hillary Clinton, saying it undermined their party's messaging on a key issue and raised questions about his ability to be the GOP's top communicator.

The California Republican, who is the leading contender to become the next speaker of the House, said Tuesday night that the GOP-led Congress had succeeded by bringing down Clinton's poll numbers because of the long-running investigation into the 2012 terror attack that killed four Americans.

"Everybody thought Hillary Clinton was unbeatable, right?" McCarthy said on Fox News. "But we put together a Benghazi special committee, a select committee. What are her numbers today? Her numbers are dropping. Why? Because she's untrustable. But no one would have known any of that had happened had we not fought."

Speaking to CNN's Wolf Blitzer on "The Situation Room," Rep. Jason Chaffetz, R-Utah, said McCarthy should apologize, saying the California Republican made an "absolutely inappropriate statement."

Speaker John Boehner, who is set to retire at the end of the month, sought to provide cover for McCarthy on Thursday. In a statement, he denied that the committee has anything to do with politics.

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"This investigation has never been about former Secretary of State Clinton and never will be," Boehner said.

Privately, Republicans were outraged by the remarks, saying the House majority leader had given Democrats unfounded ammunition to argue that the committee's investigation is squarely being driven by politics. Republicans on the committee had tried for months to keep the focus of the inquiry on the administration's handling of the attacks, avoiding getting into the ins and outs of the various aspects on the email stories.

"I might have said it differently," Rep. Darrell Issa, R-California, told CNN. "Any ancillary political activity that comes out of it is, in fact, not the goal of the committee and is not what the committee is seeking to do."

Added Rep. Justin Amash of Michigan, "I totally disagree with those comments." Asked if they could jeopardize his bid for speaker, the conservative Amash said: "I think it should be a concern."

McCarthy's comments come at a pivotal moment for the 50-year-old Republican. He is now the leading candidate to replace Boehner during next week's leadership elections, giving him a major platform to drive the national conversation and shape the agenda for the GOP. And McCarthy's Benghazi comments could reinforce the impression among some of his critics that his gaffe-prone nature could hurt the party headed into 2016.

Rep. Chris Stewart, a supporter of McCarthy's who did not see the leader's remarks, said that the California Republican may need to be cognizant that his comments now are going to be heavily scrutinized.

"Being a majority leader is different than being the speaker," Stewart said. "There is a bigger microscope."

Stewart added: "I don't think it's the goal of the conference to hurt Hillary Clinton. ... I don't think I have ever heard a single time Hillary Clinton's name mentioned in conference."

In a statement, McCarthy's office said the investigation has been aimed squarely at learning the facts.

"These inquiries have nothing to do with politics and everything to do with the consequences of what the former secretary has done and her confusing, conflicting and demonstrably false responses," said Matt Sparks, a McCarthy spokesman.

The damage control by McCarthy came on the same day that Boehner announced leadership elections would take place October 8. McCarthy only faces a nominal challenger to the post so far -- Rep. Daniel Webster of Florida -- and he still remains the odds-on favorite.

But McCarthy's GOP critics were quick to seize on his remarks to show he's unfit for the speakership.

Kentucky Rep. Thomas Massie, who supports Webster, said McCarthy's remark "diminishes" the work of Rep. Trey Gowdy, the South Carolina Republican who chairs the committee.

For his part, Gowdy described McCarthy on Thursday as "a friend," but defended the work his panel had done.

"Look, I cannot control what anyone else says, I can just control what we've done," he said. "And if you look at the hearings, her name hasn't been mentioned, if you look at the witness interviews, only three of them have any connection whatsoever."

Members of the committee were perplexed at McCarthy's statement, given it was contrary to the entire messaging strategy followed by Republicans on the Benghazi committee.

The GOP members and staff have worked to stay very disciplined to avoid the suggestions that they had political motivations. And House Republicans are quick to take credit for the fact that if it weren't for the committee, no one would know that Clinton had a private email server.

But they are staying clear of the legal debate about whether or not that practice broke any laws. Instead, Gowdy and other members of the panel say they want to ensure the committee gets all the emails that are uncovered as they relate to the attacks in Benghazi.

As the GOP members of the panel approach the October 22 public hearing with Clinton, they are planning roughly four rounds of questions but they are leaving any discussion about the email servers until the latter part of the hearing. According to a source close to the committee, the plan going into the session was to wait to bring up the email issue until the third or fourth round -- an effort to avoid any suggestions that politics was involved in the effort.

Georgia Rep. Lynn Westmoreland, a member of the Benghazi panel, downplayed McCarthy's comments as a "slip up" and predicted that they wouldn't hurt him next week when the votes are cast for Speaker.

But Westmoreland pushed back at the notion the committee's purpose was political. "That is not true at the committee, and (McCarthy) knows that's not true at the committee. Chairman Gowdy has been clear this is not about politics."

Rep. Tom Price, R-Georgia, a candidate for majority leader, said the "role of the Benghazi committee is to get to the truth."

The No. 3 House Republican, Rep. Steve Scalise of Louisiana, sidestepped CNN's questions about the blowback.

Pressed if the comments were inappropriate, Scalise dodged again and said, "the Benghazi's panel's objective from the beginning was to get all the facts. Trey Gowdy's done a great job of doing that."

But McCarthy had one defender: Rep. Bill Flores, a Texas Republican who chairs the Republican Study Committee.

"If you think about it, the American people would not know about Hillary's email server -- the lack of security she had, the transmitting of top secret messages via an unsecured server -- they wouldn't know about any of that if it hadn't been for the good work of the Benghazi committee.

"I don't believe what McCarthy said is out of line," Flores added.

Illinois Republican Rep Adam Kinzinger, a supporter of McCarthy's, told CNN that McCarthy's comments were "unfortunate" said he needs to address them.

"It was one comment. I can tell you Kevin McCarthy is very committed to getting justice, not taking down certain people on this. But I will say again, when you look at what happened after this, when you had Hillary Clinton blame this on a video, and we found out in fact this wasn't a video at all,I think there's a lot of questions to be answered."

Kinzinger added, "Now, for Kevin's statement, it's unfortunate. Probably he should make a comment."

While the Illinois Republican predicted the controversy wouldnt hurt McCarthy's chances of becoming Speaker, he suggested some conservatives critical of McCarthy may use it against him.

"We all know there's 25 troublemakers in our caucus and we'll see what they do."